If you were not allergic to anything, your lips most likely would have not been peeling.
Just a fact that your skin keeps dying continuously is actually a strong sign of allergy to something you are getting in touch every day or almost every day.
Most likely something your lips or your mouth or your digestive tract is getting in touch with every day.
One very simple way to develop a new allergy is actually to continuously bite or continuously crack your lips until they bleed.
Once you start eating or drinking or brushing your teeth, or treating your lips with something, food or toothpaste or aquaphor goes straight into your blood stream through those open sores.
Repeat it long enough and you get a new allergy, even if you never had one to begin with.